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Archive for Mathematical Logic

, Volume 56, Issue 7–8, pp 811–829 | Cite as

Equimorphy: the case of chains

  • C. LaflammeEmail author
  • M. Pouzet
  • R. Woodrow
Article

Abstract

Two structures are said to be equimorphic if each embeds in the other. Such structures cannot be expected to be isomorphic, and in this paper we investigate the special case of linear orders, here also called chains. In particular we provide structure results for chains having less than continuum many isomorphism classes of equimorphic chains. We deduce as a corollary that any chain has either a single isomorphism class of equimorphic chains or infinitely many.

Keywords

Equimorphy Embedding Isomorphic 

Mathematics Subject Classification

06A05 03C64 03E04 

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Notes

Acknowledgements

The first author warmly thanks the Logic group and their staff at the Institut Camille Jordan of Université Lyon I for their wonderful hospitality during the final preparation of this work. The second author thanks the Department of Mathematics and Statistics of the University of Calgary where this research started in the summer of 2012 and for the stimulating atmosphere and support. All three authors thank the referee for valuable comments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.ICJ, MathématiquesUniversité Claude-Bernard Lyon 1Villeurbanne CedexFrance

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